Burke-Shaw System
Burke-Shaw System art by Riccardo Zerbinati translates a time-dependent trajectory into sculptural geometry. Explore the reference equations and the path from Grasshopper to the finished digital render. Sweeping a cross-section along the sampled rail gives the mathematical trace a surface that responds to material and light.
The mathematical reference
The Burke–Shaw name identifies the nonlinear system used as this work’s point of departure. The artwork does not present itself as a scientific graph, dataset or exact simulation. It carries the system name into a visual-art context, where the reference can prompt curiosity while remaining distinct from a technical explanation.
Burke-Shaw System equations
The model combines linear feedback with two product terms. Its constant driving term b is independent of the current position on the trajectory.
Here, t is time and the variables are coordinates in the system’s state space. Letters such as a, b and c denote fixed coefficients. These are reference equations for the named model or family, not a recovered record of the parameters, initial conditions or integration settings used in this particular image. Chaotic behaviour depends on those choices.
Formula reference: View the documented system and source.
From a trajectory to Burke-Shaw System art
Riccardo develops the rail in Grasshopper for Rhinoceros using Chimpanzee. The system evolves over time, producing successive three-dimensional points. Connecting those samples creates a path. A cross-section is then swept along that rail, giving the line thickness and a surface. This is how a time-dependent mathematical trajectory becomes visible as sculptural geometry.
The sweep adds a visual layer to the mathematics: its width and orientation affect how the form catches light. Riccardo then uses 3ds Max to develop the material, camera and illumination. The finished work is a digital render of this geometry, rather than a photograph of a fabricated object. No generative AI is used to create the artwork.
To read the image, follow a single edge as it moves through light and shadow. Notice where the projected path overlaps, opens or disappears behind another surface. The rail comes from a rule evolving through time; the artist’s composition lets us experience that motion as a still image. The aim is to reveal the hidden beauty of chaos theory.
A study in form
This vertical study gives the mathematical reference a sculptural presence. The image can be approached slowly, first as a whole and then through its changing contour and reflected light. Its digitally modelled surface suggests a physical object but remains part of a rendered environment. The title offers context; the visual experience is left open to each viewer.
Riccardo Zerbinati modelled the work parametrically in Rhinoceros and rendered it in 3ds Max. It is one of 40 works in the Strange Attractors collection, created without generative AI.
Enquire about this artwork
Availability, edition and format can be discussed individually. Send an enquiry to ask about this study; no price or edition is listed until confirmed.